1. Home
  2. Chemistry
  3. Thermodynamics
  4. Free energy

16.4 Free energy  (Page 2/12)

<< Chapter < Page
  Chemistry     Page 2 / 12
Chapter >> Page >

Free energy changes may also use the standard free energy of formation ( Δ G f ° ) , for each of the reactants and products involved in the reaction. The standard free energy of formation is the free energy change that accompanies the formation of one mole of a substance from its elements in their standard states. Similar to the standard enthalpies of formation, Δ G f ° is by definition zero for elemental substances under standard state conditions. The approach to computing the free energy change for a reaction using this approach is the same as that demonstrated previously for enthalpy and entropy changes. For the reaction

m A + n B ⟶ x C + y D ,

the standard free energy change at room temperature may be calculated as

Δ G 298 ° = Δ G ° = ∑ ν Δ G 298 ° ( products ) − ∑ ν Δ G 298 ° ( reactants ) = [ x Δ G f ° ( C ) + y Δ G f ° ( D ) ] − [ m Δ G f ° ( A ) + n Δ G f ° ( B ) ] .

Calculation of Δ G 298 °

Consider the decomposition of yellow mercury(II) oxide.

HgO ( s , yellow ) ⟶ Hg ( l ) + 1 2 O 2 ( g )

Calculate the standard free energy change at room temperature, Δ G 298 ° , using (a) standard free energies of formation and (b) standard enthalpies of formation and standard entropies. Do the results indicate the reaction to be spontaneous or nonspontaneous under standard conditions?

Solution

The required data are available in Appendix G and are shown here.

Compound Δ G f ° (kJ/mol) Δ H f ° (kJ/mol) S 298 ° (J/K·mol)
HgO ( s , yellow) −58.43 −90.46 71.13
Hg( l ) 0 0 75.9
O 2 ( g ) 0 0 205.2

(a) Using free energies of formation:

Δ G 298 ° = ∑ ν G S 298 ° (products) − ∑ ν Δ G 298 ° (reactants)
= [ 1 Δ G 298 ° Hg ( l ) + 1 2 Δ G 298 ° O 2 ( g ) ] − 1 Δ G 298 ° HgO ( s , yellow )
= [ 1 mol (0 kJ/mol) + 1 2 mol(0 kJ/mol) ] − 1 mol(−58.43 kJ/mol) = 58.43 kJ/mol

(b) Using enthalpies and entropies of formation:

Δ H 298 ° = ∑ ν Δ H 298 ° (products) − ∑ ν Δ H 298 ° (reactants)
= [ 1 Δ H 298 ° Hg ( l ) + 1 2 Δ H 298 ° O 2 ( g ) ] − 1 Δ H 298 ° HgO ( s , yellow )
= [ 1 mol ( 0 kJ/mol ) + 1 2 mol ( 0 kJ/mol ) ] − 1 mol ( −90.46 kJ/mol ) = 90.46 kJ/mol
Δ S 298 ° = ∑ ν Δ S 298 ° (products) − ∑ ν Δ S 298 ° (reactants)
= [ 1 Δ S 298 ° Hg ( l ) + 1 2 Δ S 298 ° O 2 ( g ) ] − 1 Δ S 298 ° HgO ( s , yellow )
= [ 1 mol ( 75.9 J/mol K ) + 1 2 mol ( 205.2 J/mol K ) ] − 1 mol ( 71.13 J/mol K ) = 107.4 J/mol K
Δ G ° = Δ H ° − T Δ S ° = 90.46 kJ − 298.15 K × 107.4 J/K·mol × 1 kJ 1000 J
Δ G ° = ( 90.46 − 32.01 ) kJ/mol = 58.45 kJ/mol

Both ways to calculate the standard free energy change at 25 °C give the same numerical value (to three significant figures), and both predict that the process is nonspontaneous ( not spontaneous) at room temperature.

Check your learning

Calculate Δ G ° using (a) free energies of formation and (b) enthalpies of formation and entropies ( Appendix G ). Do the results indicate the reaction to be spontaneous or nonspontaneous at 25 °C?

C 2 H 4 ( g ) ⟶ H 2 ( g ) + C 2 H 2 ( g )

Answer:

−141.5 kJ/mol, nonspontaneous

Got questions? Get instant answers now!

Temperature dependence of spontaneity

As was previously demonstrated in this chapter’s section on entropy, the spontaneity of a process may depend upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:

Questions & Answers

how do you get the 2/50
Abba Reply
number of sport play by 50 student construct discrete data
Aminu Reply
width of the frangebany leaves on how to write a introduction
Theresa Reply
Solve the mean of variance
Veronica Reply
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.
kenneth
what is error
Yakuba Reply
Is mistake done to something
Vutshila
Hy
anas
hy
What is the life teble
anas
hy
Jibrin
statistics is the analyzing of data
Tajudeen Reply
what is statics?
Zelalem Reply
how do you calculate mean
Gloria Reply
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
Fisaye Reply
what is statistics
Akhisani Reply
data collected all over the world
Shaynaynay
construct a less than and more than table
Imad Reply
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Aschalew Reply
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?
Akshay Reply
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits
Akshay
1
Bright
Sorry i want to learn more about this question
Bright
Someone help
Bright
a= 0.20233 b=0.3384
Sufiyan
a
Shaynaynay
How do I interpret level of significance?
Mohd Reply
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
Owen Reply
yes what is it
Taneeya
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask